GENERAL DISCUSSION Dr. D. W. Davies and Mr. G. del Conde (University of Birmingham) said: It is disappointing that the experimental results given so far have all been interpreted in terms of semi-empirical potential surfaces. We have recently obtained some ab initio results for Li3 which are relevant to Whitehead and Grice's work on the scattering of alkali atoms by alkali diatomic molecules. They have presented a semi-empirical potential surface for LiNa, which indicates at least 5 kcal/mol stability with respect to LifNa, or Na+LiNa, and they have quoted a diatomics in molecules calculation as showing that Li, is about 9 kcal/moi more stable than Li + Li,. Other semi-empirical calculations have given the results that Na, and K3 are unstable with respect to Na+Na, and K+K2 respectively.There seems to be some doubt about the symmetries of the lowest states. We find "C,' for the equal bond length (Dmh) linear Li3, and 'B2 for the corresponding bent (1 35") Li3 (C,,). For a 45" angle we obtain ' A as the lowest state. This is in accordance with simple molecular orbital arguments. Companion et al., however, in their valency bond calculation obtained ,A1 for the most stable obtuse angled (137") isosceles triangle and 2B2 for the acute angled (34") triangle. Our results are given in table 1. They were obtained using contracted Gaussian orbitals to simulate a double zeta plus polarization Slater basis set with the ATMOL 2 programme on the Rutherford Laboratory IBM 370/195 computer. Each run required about 5 min computing time. TABLE OPEN SHELL RESTRICTED HARTREE FOCK RESULTS FOR THE ENERGY OF Lig RELATIVE TO 3Li (AW) distances/a.u.energies. -A Wlkcal mol- 1 Lil . . . Liz Liz-Li~ linear ( 1 80") bent (135') 6.0 9.0 2.51 2.41 8.0 2.79 2.66 7.5 2.94 2.83 6.5 3 .oo 3.08 6.0 (2Ez) 2.06 ('&) 2.46 5.05 - 9.0 8.0 7.5 6.5 6.0 Lit . . . Lij = Li, . . . Liz Liz-Li, 6.5 4.98 6.0 4.59 5.0 3.82 4.06 4.06 4.36 4.27 4.54 4.42 4.62 4.51 4.42 4.5 I 3.85 4.22 bent (45") 2A1 6.16 6.19 -22.3 ('B2) * 1 a.u. = 627.5 kcal/mol Basis set 1s 1s' 2s 2s' 2p 2p' 3GTO/STO. J. C. Whitehead and R. Grice, Paper in this Discussion. A. L. Companion, D. J. Steible and A. J. Starshak, J. Chem. Phys., 1968, 49, 3637 B. T. Pickup and W. Byers Brown, MoI. Phys., 1972, 23, 1189. 369370 GENERAL DISCUSSION For an unperturbed Li, molecule (bond length 5.05 a.u.) there is a small attraction for Li with a minimum energy at about 7 a.u.for both the linear (180O) and the 135" approach. The minimum is about 5 kcal/mol and the difference between the two approaches about 0.1 kcal/mol. For Liz stretched to 6 a.u. the energy of Li3 is higher than that of unperturbed Liz + Li ; but similar behaviour is found with minima at about 7 a.u. For perpendicular approach by the Li atom (45" isosceles triangle) to an unper- turbed Liz (4.98 a.u.) the energy is about 13 kcal/mol lower than for the linear ap- proach, and it is lower still for a 4.59 a.u. Liz distance. For a smaller isosceles triangle of sides 5.0, 5.0, 3.8 the energy rises sharply. These results give some support to Whitehead and Grice's conclusion that the potential surface is very flat for systems of this type ; but the low energy of the acute angled isosceles triangles, also suggested by Companion et al. ,2 requires further investigation.The reliability of single configuration molecular orbital calculations of this type, particularly for open shell systems, is an interesting question. In these calculations the energy of Li3 is a rigorous upper bound to the true energy. The energy relative to 3Li is not bounded : but experience has shown that such calculations for closed shell systems usually give a minimum with the correct ge~metry.~ They are not reliable at distances far removed from the minimum. The results reported here are first steps towards an ab initio potential surface for Li3. The energy for Liz suggests that a considerable scaling up would be desirable, and it may be that linear Li3 is about 3 kcal/mol lower in energy than Li + Li2.r I I I 1.0- K2+ 1 2 6606 8 4 8 - n A 0 v) * - - .- El G .- 8 s I 0 - (d v) - l3 8 - .CI -1.0 - 8 4 6 4 @ @ - 1 I 1 Dr. S. M. Lin and Dr. R. Grice (Cambridge University) said: We should like to report the observation of chemi-ionisation in reactive scattering potassium dimer K2 beam with a range of halogen containing of a supersonic molecules. The J. C. Whitehead and R. Grice, Paper in this Discussion. A. L. Companion. D. J. Steible and A. J. Starshak, J. Chem. Phys., 1968, 49, 3637. H. F. Schaefer, The Electronic Structure of Atoms and Molecules (Addison Wesley, 1972), pp. 325-33 1.GENERAL DISCUSSION 371 initial translational energy (E N 10 kcal/mol-l) is not greatly above the thermal energy range.The molecular beam apparatus previously used for reactive scattering measure- ments with an alkali dimer beam has been augmented with a Faraday cup ion detector placed below the scattering zone and a repeller plate above. The dependence of the ion signals measured for the K2+Iz reaction on flagging the I, beam as a function of repeller voltage is shown in fig. 1. Equal positive and negative ion signals are observed on changing the polarity of the repeller plate. There is a very rapid change close to zero volts indicating that the ions have low translational energies in laboratory coordinates. This is in accord with the low energies of the incident beams. The ion current is normalised by monitoring the dimer beam attenuation and the intensity of scattering with a surface ionisation detector. The ratio of total cross section for chemi-ionisation Qi to the total reaction cross section Qr may thus be determined.The results for K, + 12, HgC12, Hg12 are given in table 1. When the total reaction cross section Qr has been separately determined in a reactive scattering experiment, the total cross section for chemi-ionisation may be calculated as given in table 1. However Qi will in general be less accurate than the ratio Qi/Qr since total reaction cross sections Qr are not very accurately determined in crossed beams experiments. TABLE TO TOTAL CROSS SECTIONS FOR CHEMI-IONISATION Qi AND REACTION er (UNITS A”) reaction QilQr Q i Qr K2+L 1 .3 ~ - 2.0 N 150 K2 + HgC12 4 . o ~ 10-4 0.08 190 K2 + HgI2 2 . 6 ~ 10-4 0.04 140 The largest chemi-ionisation cross section Qi is exhibited by K2 +I2 where two ionisation paths (1) are energetically accessible. K2 + X,-+K+ + KX + X- (1) -+K2X+ + X-. The K, + HgX, reactions show chemi-ionisation cross sections lower by a factor N 30-50. In these reactions only one ionisation path (2) is energetically accessible. K2 + HgX,-,K,X+ + Hg +X- (2) The alternative path (3) is endoergic even with the initial translational energy E = 10 kcal mol-l. K2 + HgX2 + K+ + KX + Hg + X-. (3) Finally, no chemi-ionisation was observed for the reactions of more complicated polyhdide molecules K2+CH13, CBr,. This places an upper bound on these chemi-ionisation cross sections Qi 2 0.001 A’.Chemi-ionisation has previously been observed for reactions with high initial translational energies or with electronically excited specie^.^ However, the only P. B. Foreman, G. M. Kendall and R. Grice, Mol. Phys., 1972, 23, 117. D. R. Hardin, K. B. Woodall and R. Grice, Mol. Phys., 1973, in press. G. A. L. Delvigne and J. Los, Physica, 1972, 59,61 ; A. M. C. Moutinho, A. P. M. Baede and J. Los, Physica, 1971,51,432 ; K. Lacmann and D. R. Herschbach, Chern. Phys. Letters, 1970, 6, 106; R. K. B. Helbing and E. W. Rothe, J. Chem. Phys., 1969,51, 1607. H. Hotop, F. W. Lampe and A. Niehaus, J. Chem. Phys., 1969,51, 593 ; S. Y. Young, A. B. Marcus and E. E. Muschlitz, J. Chem. Phys., 1972,56, 566.372 GENERAL DISCUSSION previous observation of chemi-ionisation arising from '' chemical energy " of reaction appears to be the associative ionisation of uranium atoms with oxygen molecules.Prof. J. D. McDonald (University of Illinois) said : The angular distributions of methyl iodide measured by Grice et al. from reactions of methyl with halogen mole- cules, as well as earlier measurements of the angular distributions of hydrogen halides from reactions of D atoms with halogens can be explained qualitatively by a very simple model. This model should easily represent the angular distribution of pro- ducts from any reaction which satisfies two conditions. First, the attacking particle must be much lighter (about 5 times or more) than both the transferred particle and the left-over residue of the molecule. Second, the potential energy surface (the reaction being reduced to a three-body problem) must be strongly repulsive.\ 0 Due to the strong repulsion between the separating particles (in the D + I2 reaction, the DI and the I) the two fragments separate from each other along the direction toward which their line of centre points when the light particle reaches them. Thus, the scattering angle 8 is approximately equal to the angle q5 between the direction of approach of the attacking particle and a line pointing from the transferred particle to the leaving one (see fig. 1). The substrate molecule BC can be considered to be a cylindrically symmetric ovoid, divided into zones such that, if the particle A hits the molecwle in one zone (vertical shading in figure) AB may be formed, if A hits in a second zone (horizontal shading) AC may be formed, otherwise the reaction cannot occur (white part in figure).This model has been compared with classical trajectory calculations for the case D + I2 ; the I2 molecule can be considered a prolate ovoid with major-to-minor axis ratio of 1.4 : 1. LEPS-type surfaces are approximately of this form. The D +IC1 and CHz +IC1 reactions, with sideways peaked angular distributions require either a nonreaction end zone (illustrated in the figure) or a major-minor axis ratio of 4 : 1 ifthe whole molecule can react. Present experiments are incapable of differentiating these two cases. Prof. J. C. Polanyi and Mr, J, E. Schreiber (University of Toronto) said: It has been proposed 2* that the shift from backward to sideways scattering of the molecu- lar product in the series of reactions D+C12, Br2, Iz, may be indicative of reaction through progressively more-bent configurations. For the reaction D + C12, according to this hypothesis, the potential-energy surface would be such as to favour collinear approach of D to C12.For D+Iz it would favour something closer to lateral W. L. Fite and P. Irving, J. Chem. Phys., 1972, 56,4227. D. R. Herschbach, Conference on Potential-Energy Surjaces in Chemistry, ed. W. A. Lester Jr. (IBM Research Laboratory, San Jose, California ; Publication RA18, 1971), p. 44. J. D. McDonald, P. R. LeBreton, Y . T. Lee and D. R. Herschbach, J. Chem. Phys., 1972,56, 769.GENERAL DISCUSSION 373 approach. In the present Discussion Carter, Levy and Grice have reported a similar systematic shift in product angular distribution for the series CH3 + C12, Br,, 12, and have suggested that the explanation may parallel that for the D +X, series.In both series, D +X2 and CH3 +X,, the essential element in the argument is that the rapid approach of the light attacking-species, A, precludes any large amount of rotation of the molecule under attack, BC, during the reactive encounter. Following the approach of A there will be substantial repulsive energy release between B and C leading to recoil along the B-C axis ; the direction of this axis relative to the line of approach of A therefore determines the location of the peak in the product angular distribution. This sort of strong correlation between direction of approach and product scattering angle has in fact been observed in a model (called the DIPR model 3, which assumes that the repulsion between the products operates along the initial B-C coordinate ; the most favourable case for the application of this model was thought to be that in which the masses of B and C were large compared with A.The question remains whether this is indeed a tenable description of the H+X2 and CH3 +X2 reactions, and, further, whether it is a unique description. has just reported some 3D trajectory calculations for the system D + X2. He concludes (a) that a potential-energy hypersurface that favours nearly lateral approach can readily explain the results obtained for D + 12, but (6) that this explanation cannot at the present time be regarded as entirely ~ n i q u e . ~ In the course of an independent trajectory study (prompted by the Harvard group’s striking experi- mental data, and a continuing interest in the dynamics of these reactions stemming from infra-red chemiluminescence experiments) we have come to conclusions in accord with McDonald’s finding (a).In addition (c) we have examined Carter, Levy and Grice’s proposal that the dynamics of CH3 + I2 be regarded as comparable to H + 12, and have found the analogy to be a valid one. Our lateral-approach hypersurface was made up of two parts; an underlying non-directional LEPS surface (barrier height 23, = 0 for all angles of approach) with a repulsive function superimposed. The repulsion produced a barrier of E, M 10 kcal mol-’ for collinear approach by D from either end of Iz, leaving a narrow lateral channel with negligible energy-barrier.The angle between this lateral channel and the B-C axis could be adjusted. With the angle (having the centre-of-mass of I2 at its apex) set at approx. 40°, the collision energy fixed at T = 10 kcal mol-’, and reagent vibrational plus rotational states Monte Carlo selected from 300 K thermal distri- butions, 1430 trajectories were run in 3D. Of these, 209 reacted to give the differ- ential cross-section shown in fig. l(a). The scattering angle for the molecular product is 180-Oat, hence fig. l(a) shows a differential cross-section for the molecular product peaked a little backward of sideways-in accord with the experimental result. With the mass of the attacking atom increased to 15 a.m.u., in order to simulate CH3, the differential cross-section (fig.l(6)) resembled that for H+12, but with the mean value shifted significantly (though moderately) in a direction corresponding to more-backward scattering of the molecular product. The applicability of the H + I2 surface to the CH3 +I2 problem may, therefore, go even further than Carter, Levy C. F. Carter, M. R. Levy and R. Grice, Paper in this Discussion. K. G. Anlauf, P. J. Kuntz, D. H. Maylotte, P. D. Pacey and J. C. Polanyi, Disc. Faradczy SOC., 1967,44,183. P. J. Kuntz, M. H. Mok and J. C. Polanyi, J. Chem. Phys., 1969, 50,4623. J. D. McDonald, Previous comment in this Discussion. This latter conclusion is in accord with recent work by Anderson and Kung who observed sideways-peaked scattering from a virtually isotropic LEPS potential-energy surface ; J.B. Anderson and R. T. V. Kung, J. Chem. Phys., 1973,58,2477. The initial direction of approach of A defines the forward direction. McDonald374 GENERAL DISCUSSION and Grice suggested, since the H+I, (lateral-approach) surface is able to account not only for the sideways-peaked scattering but also for the moderate shift toward more- backward scattering for CH3 + I, ; i.e., this shift could be a purely kinematic (mass) effect. (The computed backward shift is not as large as that seen experimentally, but this may be connected with the fact that the trajectories were for a higher collision energy, T, than would correspond to the experimental conditions for CH3 +I2 ; enhanced T would shift the mean angle forward).In reality, of course, this kinematic shift may not be the dominant one, since we have neglected all effects due to the chemistry and structure of CH3. 40 - r( I .c) v) N $ - n 8 9 4 20- - W eat Idel2 datldeg FIG. 1 .-Computed differential cross-section versus centre-of-mass scattering angle for the atomic product of the reactions H + 12+HI + I and CH3 + 12+CH31 + I. The inset <elsin O> gives the mean angle for the differential cross-section of the atomic product. Subtract all angles from 180" to obtain the scattering information regarding the molecular product (quoted in the experimental work). Dr. J. C. Whitehead and Dr. R. Grice (Cambridge University) said: Recent laser- induced fluorescence studies of Na,, K2 produced in supersonic nozzle beams show no evidence for dimer vibrational excitation.Taking this to indicate zero vibrational TABLE 1 .-LOWER BOUNDS TO MM' PRODUCT VIBRATIONAL EXCITATION (UNITS kcaI/moI) Na+ Cs2 4 Na+ Rbz 4 Na+& 5 K+ Rbz 3 system Evib excitation of our Cs,, Rb, beams, which is below the estimate from velocity analysis and our K2 beam, which coincides with the lower limit from velocity analysis we obtain lower bounds to the MM' product vibrational excitation Evib as indicated in table 1. These should be compared with the values Evib given in our paper,4 which in the light of ref. (1) are probably overestimates. The lower bounds to Evib corres- M. P. Sinha, A. Schultz and R. N. Zare, J. Chem. Phys., 1973, 58,549. R. J. Gordon, Y. T. Lee and D. R. Herschbach, J.Chem. Phys., 1971, 54,2393. P. B. Foreman, G. M. Kendall and R. Grice, Mol. Phys., 1972,23,117. J. C. Whitehead and R. Grice, this Discussion.GENERAL DISCUSSION 375 pond to vibrational excitation of MM‘ product to -30 % of the bond energy and to -20 % of the total available energy being disposed into product translation. The estimated lifetimes of the M2M’ complexes, based on the RRK formula, would be increased to -3/v for Na+ M2 and to - 1O/v for K+Rb2. Thus our conclusion that the reaction dynamics are direct or at most involve a short-lived complex would be unaltered for Na+M2 but a life-time comparable to the rotational period might be indicated for K + Rb2. Mr. D. A. Dixon, Mr. D. L. King and Prof. D. R. Herschbach (Harvard University) said : The reaction C12 + Br2+2BrC1 is one of several interhalogen systems for which rate studies have offered evidence (tentative because of possible catalysis by moisture or surfaces) for a four-centre mechanism with a relatively low activation energy, 15-20 kcal/mol.’ According to a molecular orbital correlation diagram given by Hoffmann,2 a much larger activation barrier is expected, comparable to the promotion energy of two electrons from bonding to antibonding orbitals and thus above the I I I I I x4-x x i x Y-fY Y I Y x2+y2 - ---+-- 2 - -+f+--e-xY +XY I 1 2 1 2 w- r A A A A r-0- * * * a 2+ or A S r*+ IT* r*- fl* n*+ fl* v“-* .i.l”+ n* 7f-ff sy+ n ::%! S A s s -- * - w n-rf +‘iy 6- d SA w (r- Q r+ (r s s ..U S S (T+r (b) FIG. 1 .-Correlation diagrams for four-centre halogen molecule exchange reaction proceeding through a square planar transition-state. Symmetry planes are denoted 1 and 2 ; S and A indicate whether an orbital remains unchanged or changes sign on reflection in one of these planes.Case (a) considers only p u and pa* orbitals, (b) includes in-plane components of pn- and pn-* orbitals. The out-of-plane pr and pn* orbitak are omitted as they correlate separately. For simplicity, the diagrams assume maximum transition-state symmetry but the nodal properties which govern the qualitative correlations are similar for other planar, nonlinear geometries. P. Schweitzer and R. M. Noyes, J. Amer. Chem. SOC., 1971, 93, 3561 and work cited therein. R. Hoffmann, J. Chem. Phys., 1968, 49, 3739.376 GENERAL DISCUSSION dissociation energy of the weaker reactant bond.For C1, + Br2 this is r45 kcal/mol. Fig. I(a) shows Hoffmann’s diagram, which considers only the sigma molecular orbitals derived from the valence p orbitals of the halogen atoms. Fig. l(b) is a correlation diagram which includes the pi orbitals and shows that linear combinations of the reactant p a , pn, pn*, and pa* orbitals correlate with product px*, pa*, pa, and pn orbitals, respectively. Diagram (b) likewise predicts the reaction is “ forbidden ” for reactants in the ground electronic state. This results from the upper avoided crossing between the p n and pa* orbitals ; the lower crossing is unimportant since it involves filled orbitals. However, in diagram (a) the product p a orbitals are unfilled whereas in (b) the product pn orbitals are unfilled.A substantially lower activation energy than predicted by (a) is thus indicated by (b) ; for CI,+Br, this energy is perhaps as low as -20-30 kcal/mol. A lowering of the activation energy by vibronic interactions has also been suggested. These considerations encourage further experimectal pursuit of the halogen molecule exchange reaction. In a crossed-beam study of C12 + Br2, we have found no evidence of reaction at collision energies up to about 30 kcal/mol. The experiments employed a “ double nozzle-beam ” arrangement. The nozzle orifice diameter was 0.075 mm for C1, and 0.17 mm for Br,. The Cl, beam was “ seeded ” with helium to obtain high collision energies. In most runs a 5 % C12, 95 % He mixture was used, with total pressure within the nozzle about 1OOOTorr and the nozzle temperature varied up to about 750 K.The Br, nozzle was operated at pressures up to about 900 K. At the highest temperatures, the reactant beams contained less than 0.1 % halogen atoms, whereas the proportion of vibrationally excited molecules was -35 % for C1, and -60 % for Br, (assuming negligible relaxation during the nozzle expansion, in accord with experimental results for other systems). The reactant beams were crossed at go”, with the C12 beam modulated at 70 Hz. The scattering was observed over a 150” range in the plane of the parent beams by monitoring the BrCI+ mass peak. The counting time at each angle was usually 100 s. For the extreme conditions used here, the BrClf background was unusually large, typically -250 counts/s. However, the nominal BrCl+ scattering signals, defined as the difference of readings taken with the Br, beam flag open and closed, were only 0 to 6 -F 3 counts/s. These nominal signals showed only random scatter in replicate runs, with no features attributable to the exchange reaction.From experience with other systems, we estimate the reaction cross section to be less than 0.01 A2. Prof. J. D. McDonald (University of Minois) said : We have performed infra-red chemiluminescence experiments which measure the distribution of energy among the vibrational modes of the products of unimolecular reactions. These experiments are made possible by a new apparatus consisting of a large reaction chamber, 30 cm x 30 cm x 130 cm, a DigiLab FTS-14 infra-red Fourier transform spectrometer, and a mercury doped germanium detector.The entire apparatus (including optics) is cooled to 85 K or lower. The wavelength range is 2-14 pm. The product vinyl fluoride from the reaction F+CH,CHX where X is C1 or Br was found to have a distribution of energy among its vibrational modes which closely approximates (within - 15 %) the distribution calculated assuming a random final state distribution. There was no significant emission from the C-H stretching modes of the vinyl fluoride; the calculated value is too small to be observed. The experiments were performed at pressures sufficiently low ( N Tom) that vibrational relaxationshould be negligible compared to product removal on the 77 K walls of the apparatus. T. F. George and J.Ross, J, Chem. Phys., 1971,55,3851.GENERAL DISCUSSION 377 Fluorine atoms were produced either by microwave discharge in CF, (F atoms at 300 K) or thermal dissociation of F2 (F atoms at 1100 K). The resultant product distributions were the same at the two temperatures. We have also observed a uni- molecular intermediate, cyclooctanone, containing > 100 kcal/mol of energy above its ground state, formed by addition of O(3P) atoms to cyclooctene, which lives long enough (> The ratio of infra-red intensi- ties of the C-0 stretch and the sum of all C-H stretches agrees with calculations assuming a random state distribution. s) to travel into ow observation zone. Mr. J. T. Cheung, Prof. J. D. McDonald and Prof. D. R. Herschbach (Harvard University) said : We have studied several reactions of chlorine atoms with olefins and find examples of both statistical and nonstatistical behaviour.The intermediate chloroalkyl radicals formed in these reactions are vibrationally excited by -29 kcal mol-l, the sum of the initial collision energy, the loss in bond strength in converting from C=C to C-C (- 57 kcal mol-I) and the gain in forming the new C-Cl bond (- 80 kcal mol-l). For unsubstituted olefins, the excited radical can decay only be re-emission of the C1 atom, whereas for bromo-olefins it can also release the Br atom with substantial exoergicity, about 13 kcal mol-'. Fig. 1 shows product translational energy distributions (derived from velocity analysis data) for three such reactions which appear to be statistical : Cl+ CH,=CHBr+CH,=CHCl+Br (4 Cl+ CH3CH-CHBr+CH,CH-CHCl +Br (b) C1+ CH,-CBrCH,+CH,-CClCH, + Br (4 C1+ CH2=CHCH2Br-+ClCH,CH=CH, + Br. (4 These reactions all have large cross sections, -20-35 A.The product angular distribution (c.m. system) shows at least approximately symmetrical forward-back- ward peaking for reactions (a), (b), and (c) whereas the forward peak is more pro- nounced for reaction (4, by a factor of -3. The translational energy distributions for (a), (b), (c) are seen to agree well with those predicted by the simple statistical model discussed in the Introductory Lecture and in the Four-Centre Paper. This model is designated by the rather awkward label " RRKM +AM ", since it involves compounding the radial energy distribution in the Rice-Ramsberger-KasseI-Marcus transition-state with the centrifugal angular momentum of the departing product molecules.' The curves shown in fig.1 were calculated assuming an r6 attraction in the centrifugal barrier region (rn = 3), with no exit potential barrier. A " tight " transition-state was used, but the results differ only slightly for a " loose " one. The distributions obtained using the usual approxi- mate quantum energy level density and assuming all degrees of freedom to be " act- ive " (dotted curves) are nearly the same as distributions calculated using the classical level density and neglecting the hydrogen atoms (dashed curves). Thus, even for a model based on energy randomization in the transition-state, the quantum weighting makes the light H atoms " statistically inactive ".Reaction (a) hence is practically equivalent to the classical four-atom case (n = 4 9 , and reactions (b) and (c) to the classical five-atom case (n = 73). S. A. Safron, N. D. Weinstein, D. R. Herschbach and J. C. Tully, Chem. Phys. Letters, 1972.12, 564. G. 2. Whitten and B. S. Rabinovitch, J. Chem. Phys., 1963, 38, 2466. and one which is markedly nonstatistical :378 GENERAL DISCUSSION The translational energy distribution for reaction ( d ) is displaced upwards relative to that predicted by the statistical model. This can be attributed to the short lifetime of the collision complex, its revealed by the asymmetry of the angular distribution. The translational energy release corresponds to that expected for a classical complex with only three heavy atoms (n = 4) rather than five.I I ' I I I I I I 1 - "\J Br+ CI - Tc'+ Br 0 5 10 15 0 5 10 15 translational energy E'/(kcal/mol) FIG. 1 .-Distributions of product relative translational energy in reactions of chlorine atoms with olefins : (a) vinyl bromide, (b) 1-bromopropene, (c) 2-bromopropene and (d) ally1 bromide. Full curves from experimental data; other curves from the " RRKM+AM" statistical model for a " tight " complex : dotted curves calculated using quantum level density and including all atoms ; dashed curves calculated using classical level density but neglecting H atoms. For (d) curves are also shown for the classical model assuming only four (+) or three (A) rather than five heavy atoms (carbon or halogen) participate in intramolecular energy exchange.According to the statistical model, the anisotropy of the product angular distri- bution is governed primarily by the moment of inertia of the transition-state complex about its dissociation axis. For these reactions, the anisotropy essentially provides a measure of the root-mean-square distance of the C atoms from a line between the C1 and Br atoms. The observed anisotropy for (a), (b), (c) indicates that in the transition- state both the C1 and Br atoms are attached to the same carbon atom. This implies that the product chloro-olefin has the Cl atom attached to the C atom to which Br was originally bonded (in contrast to the usual rule which has C1 added to the less substituted C atom). For (b) and (c) this inference was verified experimentally.We found that isomeric chloro-olefin molecules can be distinguished by comparing the variations in intensity of several fragment ion mass peaks as the electron bombardment voltage is varied. This technique showed that (b), the 1-bromo-propene reaction, W- B. Miller. S. A. Safron and D. R. Herschbach. Disc. Faraahv Sm.- 1967- 44. 108 : .T. C'hprn-GENERAL DISCUSSION 379 forms elclusively 1-chloropropene whereas (c), the 2-bromopropene reaction, forms exclusively 2-chloropropene. The " RRKM+AM " model is much simpler to use than phase space theory and displays explicitly the functional dependence of the product distributions. Par- ticularly for large molecules, the results obtained are practically the same. Fig. 2 illustrates this for the F + isobutene reaction studied by Parson, Shobatake, Lee, and Rice.Two sets of curves are shown, one corresponding to the classical 5-atom case, the other to the 4-atom case. I I I I I E'lkcal mol-' FIG. 2.Distribution.s of product relative translational energy for the F + isobutene reaction as calculated for various models. A 6 kcal mol-' exit potential barrier is assumed. The phase space results are from fig. 8 of the paper by Parson, Shobatake, Lee, and Rice. 0, phase space all atoms ; x , RRKM +AM, loose complex with quantum counting ; 0, RRKM + AM, tight complex with quantum counting; - . -, phase space 4 atoms ; A, RRKM+AM, 4 atom tight complex classical. Prof. R. A. Marcus (University of IZZinois) said: I should like to comment on the interpretation of these beautiful experimental results of Lee and his collaborators.The spiked-curves in fig. 6 and 8 (and in other papers) and termed RRKM are mis- labelled. RRKM only describes the distribution of states in the activated complex region, not in the products region. To test RRKM one really needs instead measurements, direct or indirect, of lifetimes of energetic molecules. However, if one introduces some added assump- tions, one can use RRKM to make predictions of the type in fig. 6 and 8. When these added assumptions are wrong, as they surely are in the curve of Lee et al., since the latter ignores exit channel effects on the translational state distribution, the resulting theoretical curve will be wrong. These interactions change considerably the shape of the theoretical plot in fig.6 and 8. an example of an " added ap- proximation" which does not ignore exit channel interactions. Only when the In this connection I have discussed elsewhere R. A. Marcus, J. Chem. Phys., 1966,45, 2630.380 GENERAL DISCUSSION activated complex is truly “ loose ” are such interactions negligible. When, instead, the step from activated products to products’ is energetically downhill, i.e., when the reverse step has an activation energy, the activated complex is typically at least “ semi-rigid ”, and so exit channel interactions occur. (More precisely, the relation in ref. (I) was given for the reverse reaction, but one can use microscopic reversibility.) I should like to endorse thoroughly the remarks of Herschbach in this connection. When all is said and done, namely when the errors in fig.6 and 8 are corrected, one suspects that indeed only a subset of the vibrational modes may be active, perhaps for reasons indicated in my response to one of Rice’s questions. However, one has to distinguish between what has been proven experimentally and what is more con- j ect ural. Dr. J. M. Parson, Dr. K. Shobatake, Prof. Y. T. Lee and Prof. S . A. Rice (University of Chicago) said : In the past, calculations of rate constants for unimolecular reactions based on RRKM theory have almost universally adopted one dimensional reaction coordinates. While it is obvious that it is necessary to conserve angular momentum in the reaction process, it is only recently that attention has been paid to this point in the theoretical analyses.The sharply pointed distributions in fig. 6 and 8 of our paper result from calculations based on RRKM theory with the additional assump- tions that the reaction coordinate is one dimensional a d the barrier height has the value which gives a best-fit to our angular distribution data. We are quite aware that the unrealistic spike in the theoretical recurrent energy distribution is a result of the assumed one dimensional reaction coordinate and is not, per se, a failure of the energy randomization hypothesis. Our conclusions relevant to the adequacy of the energy randomization hypothesis are actually dependent on comparisons between experiment and calculations based upon the more realistic statistical phase space theory. We agree, as pointed out by Herschbach, that if conservation of angular momentum is added to the canonical RRKM theory the predictions will be very close to those of the phase space theory.In that sense, it is perhaps more appropriate to refer to the curve we have labelled phase space theory as RRKM theory. Of course, the matter of labelling is not the heart of the problem. We are aware, and we agree with those who also comment, that the recoil energy distribution of product molecules does not directly test RRKM theory, but rather that additional assumptions must be tacked on to that theory if a recoil energy distribution is to be predicted. Clearly, if the additional assumptions were unrealistic the pre- dicted distributions will be of questionable value. In the reaction of F+C2H4 to form C2H3F, there is a barrier in the exit channel which was detehned from the translational energy distribution of product molecules to be about 1 kcal/mol. The important question is how this 1 kcal/mol of potential energy will be distributed amongst the various degrees of freedom of the product molecules and how, during the process of product separation, the translational and internal degrees of freedom are coupled.These questions can not be answered in general but for a system like F + C2H4 there is an extreme asymmetry in the product masses so that the potential energy associated with the barrier should go almost entirely into translational motion. Our conclusion that the reaction complex has a non-statistical energy distribution is based on the assumption that when a light particle leaves the complex the exit channel interaction will not greatly modify what can be deduced about the distribution of states in the activated complex.Clearly, this assumption will not be valid for the case that a heavy particle leaves the reaction complex, or that a complicated particle R. A. Marcus, J. Chem. Phys., 1966,45,2630.GENERAL DISCUSSION 38 1 with internal degrees of freedom leaves the reaction complex. On the other hand for the particular case of H atom emission, the combination of small exit channel barrier and small mass lead us to believe that the deduction of the distribution of energy in the reaction complex can be quite realistic. Prof. R. A. Marcus (University of Illinois) said: The comments of Parson et al. indicate a misunderstanding of activated complex theory's and RRKM's aims and methods; perhaps it would be helpful to recall the latter.The aim of ACT and RRKM theory is to calculate a rate constant k, or a specific dissociation rate constant kEJ. Because of the quasi-equilibrium assumption, one needs to solve for such a purpose only the dynamics over an infinitesimal interval (st, sS + ds) of the reaction coordinate s ; the resulting dynamical problem is of course trivial. When in addition to calculating rates one wishes to obtain detailed information on final state distribution of reaction products, which ACT and RRKM do not try to do, one needs to solve the dynamics over a large s-interval, from sx to s = CQ. Only in the case of the loose activated complex can they be solved readily ; the result has been given in an excellent paper by Herschbach and coworkers.' When the activated complex is loose, RRKM and phase space theory become similar. To adapt RRKM one could use the statistical-dynamical treatment, which I mentioned earlier, for connecting states at Is1 = 00 with those at s = s#, or employ some other method.The problem is not solely one of disposal of some translational energy via some one- dimensional vibrational-translational mechanism. One has a coupled translational- vibrational-rotational or orbital problem which can be handled by a statistical- dynamical or other approach. When it is not loose, phase space theory no longer applies. Mr. C. F. Carter, Mr. M. R. Levy, Dr. K. B. Woodall and Dr. R. Grice (Cambridge University) said : We are seeking to extend the theory of the reactions 2-4 of atoms and radicals with halogen molecules by studying fluorine atom and oxygen atom reactions.The F atom and 0 atom beams were produced, in the molecular beam apparatus described previ~usly,~ by a microwave discharge source operating at N 0.5 Torr with CF4 and O2 gases respectively. As examples, angular distribution measurements of reactive scattering are shown for F + I2 in fig. 1, and 0 + I2 in fig. 2. The molecular orbital theory for F+XY, while formally similar to that of the halogen atom reaction Y +XY, as indicated in fig. 9 of ref. (4), may still involve considerable asymmetry due to the very electronegative F atom. Particularly for F+12 with 21 valence electrons in the configuration the 3a* orbital may be significantly F-I bonding and 1-1 antibonding, as in the H, CH, +XY Thus, a greater degree of repulsive energy release might be anticipated for F + I2 compared with the C1+ I2 stripping reaction ' 1 6and the Br + I2 reaction 6 * FII(la)2(2a)2( ln)4(2n)4(3n*)4(3a*) (1) which involves a short-lived complex.S. A. Safron, N. D, Weinstein and D. R. Herschbach, Chem. Phys. Letters, 1972, 12, 564. D. R. Herschbach, Conf. on Potential Energy Surfaces in Chemistry, W. A. Lester, ed., Santa Cruz, 1970, 44. J. D. McDonald, P. R. LeBreton, Y. T. Lee and D. R. Herschbach, J. Chem. Phys., 1972, 56, 769. C. F. Carter, M. R. Levy and R. Grice, this Discussion. Y. T. Lee, P. R. LeBreton, J. D. McDonald and D. R. Herschbach, J. Chem. Phys., 1969,51, 455 ; J. B. Cross and N.C. Blais, J. Chem. Phys., 1971,55,3970. H. J. Loesch and D. Beck, Ber. Bunse.ilges. phys. Chem., 1971, 75, 736. 2447. ' Y. T. Lee, J. D. McDonald, P. R. LeBreton and D. R. Herschbach, J. Chem. Phys., 1968, 49,382 GENERAL DISCUSSION 0 \@ A 90' 1; 0" laboratory scattering angle 0 EL30.4 t I lo3 ni s-' FIG. 1 .-Laboratory angular distribution (number density) of reactivity scattered F1 from F-t 12. n B I . ._ x 0.0 0' 30' 60' 90- 120' laboratory scattering angle 0 t 1 lo3 ni s-' FIG. 2.-Laboratory angular distribution (number density) of reactivity scattered 0 1 from 0 + 12.GENERAL DISCUSSION 383 Preliminary kinematic analysis of the angular distribution data of fig. 1 indicates intensity of reactive scattering over a broad range from sideways to backward scattering.Although velocity analysis measurements are in progress to characterise the differential cross section more precisely, the angular distribution data are in clear contrast with the sharp forward peaking of C1+12.2* The molecular orbital theory for O+XY offers a 20 electron system formally comparable with F+XY, though the electronegativity of 0 is less than that of F, comparable with C1. Moreover, the triplet ground state oxygen atom O(3P) with a singlet halogen molecule XY('C) correlates with the lowest triplet potential surface. For O+I, this has the configuration OII( I o)*(20)~( 17~)~(27~)~(37~*)~(3o*) (2) which places an electron in the 30* orbital and suggests a surface involving sufficient repulsive energy release at least to give direct dynamics, as in Cl+I,.However, a singlet potential surface, with the configuration OII( 10)~(20)~( 1 7~)~(271)~(3n*)~ (3) lies lower in energy than the triplet surface. Since the 3 8 orbital is unoccupied this should be a highly attractive surface with a potential well at small internuclear dist- ance ; indeed, OCI,, OBr, are chemically stable molecules in this electronic state. of the 0 + 1 2 angular distribution of fig. 2, shows it to be consistent with a product translational energy distribution peaking at low energy, E'wO.1 kcal mol-', with a long tail extending to higher energy and appropriate to a long-lived comple~.~ The data for 0 + I, are consistent with an angular distribution symmetric about 0 = 90°, but velocity analysis measurements are in progress to confirm this.for O+Br, are also con- sistent with a long-lived cornple~.~ Hence, the O+Br, data agree with the more sophisticated velocity analysis measurements of Herschbach.6 Thus it appears that the O+Br,, I, reactions may undergo a transition from the initial triplet surface to the lower singlet surface. However, our measurements for O+ICl, where 0 1 is the predominant reaction product, preclude a transition to the singlet surface in this case, since OCl would then have been the preferred reaction product (see the comment by Dixon, Parrish and Herschbach). Kinematic analysis Our angular distribution measurements Dr. Y. C. Wong and Prof. Y. T. Lee (University of Chicago) said: We are quite interested in the report of Grice et al. on the F+12 reaction, since we also carried out experiments on this reaction some time ago.Our experiment was performed under somewhat different conditions ; F atoms were produced by thermal dissociation of F2 in a nickel oven rather than by microwave discharge, resulting in a slightly higher collision energy in our experiment. In contrast to a thermally distributed F beam used by Grice et a!., in our experiment the velocity of faster fluorine atoms was selected by a slotted disc velocity selector with full width A full account of this work will be submitted to Mol Phys. Measurements have also, been made on F+Ir by Y . T. Lee (private communication). Y. T. Lee, J. D. McDonald, P. R. LeBreton and D. R. Herschbach, J. Chent. Phys., 1969, 51, 465; J. B. Cross and N. C. Blais, J. Chern. Phys., 1671, 55, 3970.H. J. Loesch and D. Beck, Ber. Bimsenges. phys. Chem. 1971, 75, 736. F. A. Cotton and G . Wilkinson, Adiwnced hiorganic Chemistry (Wiley Interscience, N.Y. 1962). S. A. Safron, N. D. Weinstein, D. R. Herschbach and J. C. Tully, Chem. Phys. Letters, 1972, 12, 563. D. R. Herschbach, this Discussion, Introductory Lecture.384 I I I I I I I F + I i - IF t I ' I I I - - GENERAL DISCUSSION laboratory scattering angle, 0 FIG. 1.-Laboratory angular distribution of IF from F+12. E I E total E'/kcal mol-' FIG. 2.-Centre-of-mass angular and energy distributions which give best fit to the data shown in fig. 1.GENERAL DISCUSSION 385 half maximum of 20 %. Consequently, our experimental conditions are much better defined. The laboratory angular distribution of IF is shown in fig.1 and the best fit centre of mass energy and angular distributions for the data shown in fig. 1 are presented in fig. 2. These results are in contradiction with what has been concluded in the preliminary kinematic analysis of Grice et al. The angular distribution of IF in our experiment is nearly isotropic, with a mild forward peak somewhat more pronounced than the backward peak ; this result contrasts with the distribution of a broad range from sideways to backward as Grice et al. stated. The energy distribution of product molecules indicates that most of the exoergicity should be in vibrational motion of IF, unless a significant amount of I*(2P+) is formed in this reaction. The average translational energy is only about 15 % of the total energy available.This conclusion also does not substantiate Grice et al.'s anticipation from a simple molecular orbital consideration that a greater degree of repulsive energy release should be observed for F + I2 compared with the C1+ I2 and Br + I2 reactions. One should be extremely cautious in the interpretation of angular distributions from a " primitive experiment " in which both beams have thermal velocity distri- butions, since both cross sections and angular distributions might depend on relative velocities of reactants, rather strongly in many reactions. Thus the conclusions derived could be quite erroneous except for some favourable cases. The only experiments which will give unambiguous results are those experiments in which both beams are velocity selected and the product velocities are also analyzed.Mr. C. F. Carter, Mr. M. R. Levy, Dr. K. B. Woodall and Dr. R. Grice (Cambridge University) said : We are very interested in the report of Wong and Lee on the F+I, reaction. The centre of mass angular and velocity distributions fitted to their laboratory angular distribution data, at initial translational energy E = 1.93 kcal mol-l, have been compared with our laboratory angular distribution data at lower initial translation energy, E-0.7 kcal mol-l. Agreement could not be obtained by including any " reasonable " dependence of the total reaction cross section on the initial velocity of F atoms. Indeed, matching to our data with the centre of mass angular distribution of Wong and Lee necessitates a product translational energy distribution displaced to significantly lower energy (peaking at E'N 1 kcal mol-') for scattering in the forward hemisphere.Thus the F+12 reactive scattering appears to depend appreciably on initial translational energy in this energy range. Simple molecular orbital theory does not give an unequivocal prediction of the energy disposal. The repulsive energy release fostered by the 3a* orbital will be offset by increased charge transfer interaction in F + 12, which enhances attractive energy release. The kinematic analysis of our data indicated that the product translational energy distribution peaks below E' = 5 kcal mol-I (or < 15 %) in accord with the conclusions of Wong and Lee. Mr. D. A. Dixon, Dr. D. D. Parrish, and Prof. D. R. Herschbach (Harvard Univer- sity) said: We have also been interested in the possibility of transitions between triplet and singlet potential surfaces in reactions involving oxygen atoms.This question was posed by results for the reaction Ba('S,)+ 02(3C;) + BaO('Z)+O(3P,). The reaction is exoergic by -20 kcal mol-' but proceeds via a long-lived complex even at collision energies of - 18 kcal mol-I.' If the long-lifetime is attributed to an H. J. Loesch and D. R. Herschbach, J. Chern. Phys., 1973 (to be published). 55-N386 GENERAL DISCUSSION attractive basin in the potential surface, as usual, the dissociation energy of the BaO, complex inferred from unimolecular decay theory is quite large, 5 150 kcal mol-' with respect to the reactants. There is infra-red spectroscopic evidence for an ionically bound Ba+O; molecule.' The bond strength is unknown, but empirical correlations suggest values in the range 100-150 kcal mol-I.The spectra indicate a strongly bent molecule, with C,,, symmetry. The usual molecular orbital description thus predicts a singlet ground state, since the number of electrons is even and a bent triatomic molecule has nondegenerate orbitals. However, the reactants approach and the products depart on a triplet potential surface. This suggests that the reaction may involve switching from the initial triplet surface into the singlet basin and then back to the final triplet surface. The long complex lifetime might depend largely on those switches rather than the depth of the basin. On the other hand, a triplet ground state for Ba+O; cannot be ruled out.The electron-jump gives a triplet configuration, Ba(t4) + O,(tt)+Ba+(t)O;(lff). The elementary molecular orbital procedure is not reliable when comparing singlet and triplet states.2 For example, CH, is a strongly bent molecule but has a triplet ground state which corresponds to an excited molecular orbital c~nfiguration.~ For BaO, the question may be resolved by an e.s.r. matrix isolation e~periment.~ A similar situation obtains for the reaction O(3Pg)+BrZ(1Z:) -+ Br0(211)+Br(2P,). As discussed in the Introductory Lecture, this again proceeds via a long-lived complex. The reactants approach on a triplet surface, whereas the products can depart on either a singlet or triplet surface. A stable OBr, molecule is known, with C2,, symmetry and probably a singlet ground state.However, two arguments indicate that the surface corresponding to this symmetric OBr, is unlikely to govern the reaction. As in the reactions of hydrogen atoms or halogen atoms with halogen molecules, orbital correlations predict that insertion of the 0 atom into the Br, bond will be inhibited by a substantial energy barrier.5 The " electronegativity ordering rule ", derived from the Walsh scheme and supported by much empirical evidenc~,~ also predicts that O+Br, goes via end-on attack rather than by insertion. According to this rule, the preferred geometry of an XYZ complex has the least electronegative atom in the middle. These considerations suggest that the reaction proceeds predominantly via an 0-Br-Br complex.The analogous 0-C1-Cl molecule has been found. In a matrix isolation study,6 and the isoelectronic (F-Cl-Cl)+ ion is also known.7 An 0-Br-Br complex, even if considerably nonlinear, might well have a triplet ground state. In constructing his diagrams, Walsh emphasized that the a*'-3a* orbital (see fig. 10 of the paper by Carter, Levy, and Grice) might cross the a"-3n* and a's-37F orbitals and lie below them at large bond angles. If so, even the elementary molec- ular orbital analysis predicts a triplet ground state at cc = 180" and in a better approxi- mztion this might well remain the ground state at a- 150". The orbital configuration S. Abramowitz and N. Acquista, J. Res. Nat. Bur. Staid, 1970, 75A, 23. L. C. Allen, in Sigma A4olecular Orbital Theory, 0.Sinanoglu and K. B. Wiberg, eds. (Yale Univcisity Press, New Haven, 1970), p. 227. C. F. Bender, H. F. Schaefer, D. R. Franceschetti and L. C. Allen, J. Amer. Chern. Soc., 1972, 94, 6888. D. M. Lindsay, work in progress, Harvard University. J. D. McDonald, P. R. LeBreton, Y. T. Lee and D. R. Herschbach, J. Chem. Phys., 1972, 56, 769 and papers cited therein. M. M. Rochkind and G. C. Pimentel, J . Cheni. Phys., 1967, 46, 4481. ' R. J. Gillespie and M. J. Morton, Znorg. Chem., 1970, 9, 811.GENERAL DISCUSSION 387 of this triplet state is . . . (30*)~(3n*)~ or . . . (3c~*)~(a’s)(a’’) whereas the singlet discussed by Carter, et al. is . . . (371”)~ or . . . ( a ’ ~ ) ~ ( a ” ) ~ . We have carried out a CNDO-UHF calculation for triplet linear 0-Cl-Cl and indeed find the 30” orbital energy to be about 24 kcal mol-’ below the 3n* orbital.Accordingly, it is at least plausible that O+Br2 goes via a triplet 0-Rr-Br surface. The electronegativity rule suggests some interesting chemical variations. The O+IX reactions, with X = C1 or Br, would be expected to yield primarily IO+X rather than XO + I, although the latter path is much more exoergic. We find IC1 and IBr indeed give I 0 with a large cross section but no detectable C10 or BrO. The 0 + F2 reaction would be expected to prefer the symmetric OF2 geometry rather than 0-F-F, since oxygen is less electronegative than fluorine. Thus, despite the fact that O+F2 is much more exoergic than the other O+halogen reactions, it seems likely to require a relatively large activation energy.Experiments to test this are planned. We have also studied the 0+Cl2 and 0 + 1 2 reactions, although not yet with velocity analysis. For 0 + C1, the angular distribution is compatible with the collision complex mechanism if an activation energy of 3 kcal mol-’ is included, in accord with a flow-tube study., For O+I, the angular distribution is accurately predicted by the same statistical complex model used for the 0 + Br, case. Dr. G. Hunter (York University) (communicated): In the study of molecular dynamics there is an apparent dichotomy between rigorous theory on the one hand, and semi-empirical interpretation of experimental measurements on the other. The interaction potentials inferred from the latter approach tend to be much simpler than those involved in precise theoretical calculations.The work of Bunker and Goring- Simpson on alkali-methyl iodide reactions is a good example of this dichotomous situation. Their results, together with those of other theoretical calculations reported here, support the view that the three methyl hydrogen atoms make no effective contri- bution to the dynamics of the reaction. This conclusion supports the semi-empirical approach. I would like to present a new quantum mechanical idea which resolves this appar- ent dichotomy. To be explicit, let us consider alkali-methyl iodide collisions. First of all for simplicity consider elastic collisions. Denote the reaction co-ordinate (alkali atom-methyl iodide distance) by R, and the remaining co-ordinates (all electronic plus rotational and vibrational within the CHJ molecule) by r.We assume that the scattering angle 8 has been separated out. Then the idea is that the total wave function for a particular angular momentum state Y l ( R , r ) may rigorously be expressed as a product of an unbound (scattering) radial wave functionfi(R), and another function $(r, R) such that V(R) = (4IHl4)r is the potential function for the scattering process. H is the total internal hamiltonian (with the 8 dependence replaced by 1(1+ 1)/2pR2 iiiclzrding the kinetic energy operator associated with R. The subscript r on the expectation value (41H14)r denotes integration over the coordinates Y. In statistical terms +(r, R) is interpreted as a conditional probability amplitude. It is essentially defined variationally by the expectation value ( 41Hl+)r.In the case of an atom-atom collision (A-B), I’ would simply be the set of electronic co-ordinates, so that 4(r, R) is the electronic wave function, and V(R) is the adiabatic Born-Oppenheimer potential for the corresponding electronic state of the diatomic Subsequently, we have learned of flow tube studies in which O+F2 gave no detectable reaction under conditions where O+Br2 gave a very large yield. See M. Kaufman and C. E. Kolb Chem. Znstr., 1971, 3, 175. M. A. A. Clyne and J. A. Coxon, Trans. Faruday SOC., 1966, 62, 2175.388 GENERAL DISCUSSION molecule A-B. +(r, R) and Y(R) would actually differ slightly from the usually defined electronic wave function and adiabatic potential in so far as (+IHl+)r is the expectation value of the total internal hamiltonian rather than just the electronic hamiltonian. In the alkali-methyl iodide case V(R) is obtained by additionally integrating over the rotational and vibrational coordinates of CH31.Thus in this case V(R) involves an appropriately weighted average over all of the possible orientations and phases of the CH31 internal motion. For an experiment involving oriented molecules, such as that reported by Brooks, the orienting external field would have to be included in the hamiltonian H in order to calculate the appropriate radial potential V(R). For a particular exit channel there will be a corresponding internal state +‘(I-, R) and a potential V’(R) = (+‘IHl+’)r. The whole scattering process (into one exit channel) is thus describable in terms of two radial potentials V(R) and V’(R). The incoming and outgoing channels are connected by the uniqueness of the total wave function : that is f(R)+(r, R) =f’(R)+’(r, R) for values of the coordinates where V(R)= V‘(R). In the absence of electronic excitation this matching procedure would be virtually independent of the electronic coordinates in r. The further extension to reactive collisions is simply that the reaction (radial) coordinate in the exit channel is R’ (different from R), so that the internal coordinates of the resulting fragments (r’) are not all the same as those in the incoming channel. The radial potential for the exit channel is in this case V‘(R’) = (+’IHl$’)rp. As for inelastic collisions there is a matching condition f ( R ) 4 ( r , R) = f’(R’)+’(r’, R’) in the reaction zone. If the reaction produces three rather than two fragments, then R’ represents the relative coordinates (two distances and an angle) of the separating fragments, so that V’(R’) is a surface rather than a radial potential. The importance of this theoretical idea is that it shows that all two-body collision processes (the bodies being atoms or molecules) are describable in terms of one or tow radial potentials V(R) and V’(R’) : it really isn’t necessary to consider the dynamics of all of the atomic nuclei on a multi-dimensional potential energy surface. This will considerably simplify classical trajectory calculations as well as quantum mech- anical methods. Ab initio calculation of the radial potentials V(R), V’(R’) is of course a formidable problem : some kind of super Hartree-Fock procedure is indi- cated. On the other hand, determination of these potentials semi-empirically from experimental data is now seen to be a theoretically sound procedure. The description of collisions in terms of potential profiles (presented by Prof. Polanyi in his Concluding Remarks) is also placed on a sound theoretical basis by this theory : the profiles are to be interpreted as the potentials V(R), V’(R’) defined above, rather than as sections through the multi-dimensional potential energy surface. Thus this theory unites the semi-empirical approach (notably propounded by Herschbach during this meeting) with the rigorous approach of the pure theoretician. The formal aspects of this theory will be presented for publication in the near future. The extension to inelastic scattering is fairly straightforward.